Estimate center or axial field for multiturn loops. Use unit controls and instant scientific outputs. Download reports, inspect graphs, and compare sample field values.
Example conditions: current = 4 A, turns = 18, radius = 0.10 m, relative permeability = 1. The table shows axial field values at several distances.
| Axial Distance (cm) | Axial Distance (m) | Magnetic Field (T) | Magnetic Field (µT) |
|---|---|---|---|
| 0 | 0 | 0.000452389 | 452.389342 |
| 2 | 0.02 | 0.000426543 | 426.542545 |
| 4 | 0.04 | 0.000362097 | 362.097379 |
| 6 | 0.06 | 0.000285236 | 285.23578 |
| 8 | 0.08 | 0.0002154 | 215.400443 |
| 10 | 0.1 | 0.000159944 | 159.943786 |
B(0) = (μ0 × μr × N × I) / (2R)
B(x) = (μ0 × μr × N × I × R²) / [2(R² + x²)^(3/2)]
A = πR²m = N × I × A
dB/dx = -3μ0μrNIR²x / [2(R² + x²)^(5/2)]
This calculator assumes a circular loop, steady current, and measurement along the central axis. The relative permeability factor models a simple magnetic material effect.
Then more than one segment would feel a magnetic force. You would add the vector forces on each segment. Depending on current direction and field direction, the loop could experience a larger net force, a torque, or both.
A current loop in a uniform field experiences a torque that tries to align its magnetic moment with the field.
The torque magnitude is τ = N I A B sinθ.
The net translational force is zero in a perfectly uniform field.
Iron has high magnetic permeability. It becomes magnetized and channels magnetic flux more effectively than air. That raises the magnetic field inside and near the loop compared with an air-core loop carrying the same current.
You induce an electromotive force. If the loop is closed, that emf can drive an induced current. This is Faraday’s law of electromagnetic induction.
The magnitude at the center is B = μ0 N I / (2R) for an air-core loop.
The direction is perpendicular to the loop’s plane and is found with the right-hand rule.
Curl your fingers with current; your thumb gives the field direction.
It is called a coronal loop. These bright arches of hot plasma trace solar magnetic field lines between opposite magnetic regions.
Use the center-field relation B = μ0 N I / (2R), or include μr for a magnetic core.
The exact numerical value depends on the figure’s current, radius, turns, and material.
For a circular loop, the center field is B = μ0 μr N I / (2R).
More current, more turns, or higher permeability increases the field.
A larger radius reduces it.
Along the axis, the field falls with distance according to
B(x) = μ0 μr N I R² / [2(R² + x²)^(3/2)].
It is strongest at the center and weakens smoothly as you move away.
Each turn contributes magnetic field in the same direction along the axis. When turns are closely packed, their fields add, so the total field is roughly proportional to the number of turns.
A larger radius spreads the same current path over a wider circle. That lowers the center field because the field strength is inversely proportional to radius for the center formula.
Relative permeability scales the field to approximate a magnetic material effect. Use 1 for air. Values above 1 model materials that strengthen magnetic flux around the loop.
The axial field depends on x², so positions at +x and -x give the same magnitude.
That makes the ideal axial field graph symmetric about the loop center.
Any supported unit works because the calculator converts inputs internally. Using meters and amperes often makes the formulas easier to verify by hand and compare with textbook values.
No. This version is designed for the loop center and points on the central axis only. Off-axis field calculations require more advanced expressions involving elliptic integrals.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.